The enhancement of the Raman light scattering signal from the surface of the porous hybrid biocomposites based on polyhydroxybutyrate (PHB), calcium carbonate (CaCO3), and nanoplasmonic Ag particles is investigated. Based on PHB, fibrous scaffolds are obtained by the electrospinning technique. The fibrous scaffolds have been covered by CaCO3 and Ag nanoparticles by means of mineralization in salt solutions and Ag reduction reaction. Successful formation of the CaCO3 and Ag nanoparticles on the scaffold surface has been confirmed by the data of scanning electron microscopy, x-ray diffraction analysis, and infrared spectroscopy. Surface-enhanced Raman spectroscopy (SERS) of the obtained sample surface has demonstrated a significant enhancement of the Rhodamine 6G signal (Ef > 105) in comparison with the reference sample where the analyte concentration and the laser power were 100 times higher. Thus, the present research has confirmed prospects for the application of biocomposites based on polyhydroxybutyrate for detection and investigation of biomolecules by the SERS method.